Well this is not very helpful but to state the obvious, have you tried restoring the iPad? Since the pc doesn't see it then maybe you should restore to factory settings from the iPad itself. That's what I would do anyway but no idea if it will help or not.
My iPad 1 is like "frosen". I succeeded to shut it down, but turning it on, I see an apple and a little later "the gear" trying to start. Then everything stops ;/ Anyone who
can help me???? Please ...